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Hindawi Publishing CorporationAdvances in BioinformaticsVolume 2011, Article ID 184731, 11 pagesdoi:10.1155/2011/184731

Research Article

Data-Driven Compensation for Flow Cytometry of Solid Tissues

Nickolaas Maria van Rodijnen,1 Math Pieters,1 Sjack Hoop,1 and Marius Nap1, 2

1 Department of Pathology, Atrium Medical Centre, P.O. Box 4446, 6401 CX Heerlen, The Netherlands2 TiCC, Tilburg University, Warandelaan 2, 5037 AB Tilburg, The Netherlands

Correspondence should be addressed to Nickolaas Maria van Rodijnen, [email protected]

Received 3 February 2011; Revised 20 May 2011; Accepted 8 June 2011

Academic Editor: Shandar Ahmad

Copyright © 2011 Nickolaas Maria van Rodijnen et al. This is an open access article distributed under the Creative CommonsAttribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work isproperly cited.

Propidium Iodide is a fluorochrome that is used to measure the DNA content of individual cells, taken from solid tissues, with aflow cytometer. Compensation for spectral cross-over of this fluorochrome still leads to compensation results that are dependingon operator experience. We present a data-driven compensation (DDC) algorithm that is designed to automatically compensatecombined DNA phenotype flow cytometry acquisitions. The generated compensation values of the DDC algorithm are validated bycomparison with manually determined compensation values. The results show that (1) compensation of two-color flow cytometryleads to comparable results using either manual compensation or the DDC method; (2) DDC can calculate sample-specificcompensation trace lines; (3) the effects of two different approaches to calculate compensation values can be visualized withinone sample. We conclude that the DDC algorithm contributes to the standardization of compensation for spectral cross-over inflow cytometry of solid tissues.

1. Introduction

Multiparameter flow cytometry (MP-FCM) of solid tumorsis a powerful tool for quantification of antigen expressionand DNA content, based on large numbers of individualmammalian cells. However, simultaneous application of dif-ferent fluorochromes introduces spectral cross-over. Spectralcross-over is the acquisition of fluorochrome intensities froma primary fluorochrome in the detector(s) used to acquirethe intensity of secondary fluorochromes. Compensationis the estimation of the amount of fluorochrome intensitythat needs to be subtracted from the acquired intensities tocorrect for spectral cross-over [1–4]. Proper compensationis achieved when the compensated data in the cross-overdetector has no bias in the fluorescence distribution that isrelated to the intensity measured in any other detector [5]. Toachieve proper compensation, the amount of spectral cross-over of each fluorochrome in a flow cytometry panel canbe estimated with a single stained control (SSC). An SSCconsists of a single cell suspension of which the individualcells are labeled with only one fluorochrome. This fluo-rochrome, of which the intensity is acquired in its primarydetector, exhibits spectral cross-over in other secondary

detectors. The cross-over of the SSC in each secondarydetector is expressed as a percentage of the intensity acquiredin the primary detector. This percentage is based on thecorrelation coefficient between the fluorochrome intensity ofa SSC in the primary and secondary detector(s) [1, 3]. Thecombination of all the percentages cross-over for each SSC,in each secondary detector, is expressed in a compensationmatrix. It is common to calculate this compensation matrixonce or twice a day and to use it for all following acquisitions.

The problem of flow cytometry when working with cellsoriginating from solid tissues is the use of propidium iodide(PI). PI is a dye that binds to DNA, and the acquired intensityis proportional to the amount of DNA in a (tumor) cell.The major advantages of PI are that (1) the DNA profileof the acquired (tumor) cells can be studied in relationto their phenotype, (2) it is possible to get very smallcoefficients of variation (CV) even in paraffin embeddedmaterial, in contrast to other DNA dyes like TOPRO3 and,(3) PI doesnot stick to the interior of the flow cytometer,like DAPI does. The major disadvantages of the PI dye are(1) spectral cross-over in all detectors that primarily detectfluorochromes excited with 488 and 635 nm lasers and (2)it binds noncovalently to DNA. The loose binding makes

2 Advances in Bioinformatics

compensation case specific because the average amount ofbound PI is also dependant on the number of cells ina single-cell suspension. When the number of cells variesfrom case to case, the acquired average intensity of PIvaries, and therefore the primary detector of PI needsvariable amplification. Variable amplification of detectors ina flow cytometry system disturbs compensation matrices.Therefore each case needs its own compensation matrix. Asa consequence compensation needs to be performed for eachcase separately. This is time consuming and therefore costly.

In this paper we investigate spectral compensationusing an algorithm we called Data-Driven Compensation(DDC) which is especially developed to deal with variablecompensation matrices when PI is used to study the DNAcontent of (tumor) cells in a single-cell suspension. Wedescribe the analysis steps of the automated compensationconcept based on the data of a 2-color experiment. In 2-color flow cytometry each event or count represents theacquired fluorochrome intensities for the 2 colors of onecell. The main difference between the DDC method andknown compensation algorithms is based on the fact thatDDC calculates the compensation values on automaticallyselected counts. The key characteristic of the selected countsis that they all have the same primary fluorescence. Thisfeature reduces the value spread of the counts that areselected to calculate the correlation between the acquiredfluorochrome intensities in the primary PI detector anda secondary detector. The reduced spread of these countsthus opens the possibility of automatically compensationfor spectral cross-over from PI, avoiding the need for anymanual intervention.

2. Material and Method

2.1. Patient Population. Over the period of January throughDecember 2007 we analyzed 227 lymph node biopsies thatwere obtained from sentinel lymph node (SLN) proceduresin breast cancer patients [6]. The SLNs were routinelyexamined at 3 levels with steps of 500 µm by a pathologistfor (micro)metastasis. Each examined level consisted of a3 µm, H&E stained section and processed for histology.These 3 levels are reached by taking 10 sections of 50 µmbefore the next H&E level. All four 50 µm sections werecollected in a glass tube and processed for flow cytometry.For a detailed description of this procedure see [6, 7]. Inbrief, a single cell suspension of individual lymph nodecells was generated from the four 50 µm sections anddivided in two separate samples; one served as negativecontrol (NC) and was incubated with 2 µL of a nonrelevantmouse monoclonal antibody isotype IgG1 (X 0931, DAKO;diluted 1/20); the second one served as test sample (TEST)and was incubated with 2 µL of a cytokeratin monoclonalantibody isotype IgG1 (clone MNF116; M 0821, DAKO;diluted 1/20, DAKO). The nonrelevant mouse monoclonalantibody served as isotype negative control to determine theamount of nonspecific antibody binding, and the cytokeratinantibody labels epithelial metastatic cells in the TEST. Afterovernight incubation the two single-cell suspensions werewashed twice with PBS (pH 7.4) and incubated with a

polyclonal goat antimouse FITC (F 0479, DAKO, undiluted)for 1.5 hours, followed by another two washing steps. Afterthese last washing steps 1 mL PI (1 µg/mL, Sigma) was addedfor DNA labeling. When the antigen expression detected viathe FITC signal in the TEST sample passed a given threshold(1% positive events), a sample was considered positive formetastasis, based on previous experience [8]. The height ofthe threshold was set on the NC and contained exactly 0.5%FITC-positive events above this line. In the positive casesthe acquired DNA histogram provided information aboutthe ploidy status of the metastasic material in relation to theFITC-positive events.

2.2. Data Set. To ensure comparability of individual casesdata files, 190 of a total of 227 data sets were selected based ona minimum of 100.000 counts acquired for both the NC andTEST files. A further 38 cases were excluded from the dataset because of a laser replacement and laser beam alignmentoptimization, leaving a total of 152 cases to enter the finaldata set.

2.3. Data Acquisition. All flow cytometric acquisitions wereperformed on a BD FACSCalibur (BD Biosciences, SanJose, CA) flow cytometer with a single 488 nm argon laser.Forward light scatter, right-angle (side) scatter, and twofluorescence signals (FITC and PI) were acquired simulta-neously in list mode. The fluorescence was measured usingthe standard photomultipliers (PMTs) and optical filters(530/30 nm BP filter for FITC and 670 nm LP filter for PI).The forward scatter was recorded with a photo diode. ForFITC emission the pulse height was recorded (FL1h), forPI emission, in addition to the pulse height (FL3h), alsothe pulse width (FL3w), to calculate the area (FL3a), wasacquired.

For each sample 100.000 counts were acquired, triggeredon FL3. The DNA content was recorded in linear modewith a resolution of 1024 units. The FITC expression of thecells was recorded in logarithmic mode with 4 log decadesin a range of 100 to 104, also using a resolution of 1024units. No hardware compensation was performed duringflow cytometric acquisition.

2.4. Data Analysis according to Standard Available Procedures.For the analysis of the flow cytometric data files the softwarepackage Summit V 4.0. (DakoCytomation, Glostrup, Den-mark) was used. Selection of single cells was accomplishedby setting a region in a dot plot of FL3-w (abscissa) againstFL3-a (ordinate) of the PI parameter for the NC and TESTseparately. As a standard procedure, the height of the singlecell region was set to include the 2C, 4C, 6C and 8C ploidyclusters. These four clusters represent cells in, (1) the diploidG0/G1 (2C) mode; (2) the combined G2M-phase (4C)—diploid cell cycle—plus tetraploid G0/G1 cells; (3)-(4) twoaggregate peaks (6C and 8C), with the 8C peak containingcells in the G2M phase of the tetraploid cell cycle. Thefour clusters are identified in Figure 3(a). If an aneuploidpopulation with a DNA index (DI) above value “2” would bepresent in the FL3-a DNA histogram, the height of the single-cell region could be expanded to include the aneuploid G2M

Advances in Bioinformatics 3

peak. This aberration could not be identified in the presentdataset. There is no objective criterion to set the width of thesingle-cell region [9], and therefore it is determined by theoperator. However, analysis revealed that all applied single-cell regions include 70–80% of the total amount of counts,both for the NC and the TEST.

In the standard procedure, not data-driven, compen-sation for spectral cross-over is accomplished using a dotplot of FL3a-PI (abscissa) against FL1h-FITC (ordinate), byentering a percentage (compensation value) in the com-pensation matrix of the Summit software. As stated before,correct compensation is achieved when the compensatedFITC intensity has no bias in the fluorescence distributionthat is related to the acquired PI intensity. Since spectralcompensation leads to compensation artifacts [1, 3, 5, 8,10], commonly the median values of individual cell clustersare compared to determine the amount of intensity relatedbias in compensated dot plots. However, in PI acquisitionsaround 80% of all the counts are located in the 2C cluster.Therefore we choose to compare the median value of the2C cluster with the median value of the combined counts inthe 4C, 6C, and 8C clusters. Therefore the compensated dotplot is divided in 2 regions that are separated by a verticalline. This line is set to separate the 2C cluster on the lefthand from the 4C, 6C, and 8C clusters on the right hand.This region setting serves in comparing the median valuesobtained for each region of the dot plot. When the twomedian values differ too much after operator activation ofthe compensation value, this initial value is adjusted and thecompensation operation is performed again. As indicatedalready above, after compensation of the NC sample, ahorizontal cut-off line is set in the dot plot, allowing no morethan 0.5% FITC-positive counts to exceed this thresholdvalue. The same compensation settings are applied to theTEST sample data. If the compensated TEST data show anincreased or decreased median value for the 2C cluster ascompared to the median value of the combined 4C, 6C,and 8C clusters, the compensation value is adjusted, beforeapplying the same cut-off line as defined above. In ourhands, this adjustment was only required in cases with largemetastasis (>2.0 cm) resulting in a higher intensity of theFITC signal. When the percentage of positive cells (countsabove the cut off line) in the TEST sample exceed 1.00%the sample is considered positive. The following data werecollected: (1) the compensation values for the NC and TESTsamples and (2) the percentage of MNF116-positive cells(counts above the threshold) in the TEST sample, (3) DNAploidy.

2.5. From Standard Compensation Procedures to Data-Driven Compensation. This section describes the theoreticalbackground that stimulated us to develop a data-drivenapproach for compensation of spectral cross-over comparedto hardware-driven or operator-dependant methods. Thetotal fluorescence intensity detected by a primary fluores-cence PMT in a 2-color flow cytometer setup consists offour contributions: (1) the fluorescence signal of the primaryfluorochrome, (2) the cellular autofluorescence [11], (3) theoptical and the electronic noise generated in the cytometer

[4, 5], and (4) the cross-over signal from the secondaryfluorochrome [1] also called the intensity-dependent bias [5].The aim of the compensation step is the determination ofthe sole contribution of the primary fluorescence, within thetotal fluorescence intensity measured. Autofluorescence andnoise contribute to the variance of the overall fluorescencesignal. The autofluorescence also increases the intensityof the overall fluorescence signal. Both autofluorescenceand noise are inevitable. They can be minimized, as wewill show later, but cannot be offset by a mathematicalcompensation. In contrast to this complexity, the estimate ofcontribution of the cross-over to the total signal intensity canreadily be performed by an experienced operator by visualinteraction.

To confirm and visualize this intensity-dependent bias,operators plot the fluorescence intensities as detected bythe primary PMT against those detected by the secondaryPMT. The resulting dot plot contains an approximately lineardistribution of points with the intensity-dependent biasexpressed as the slope of the distribution [1]. It is thus keyto define or calculate the value of this slope of the intensitydependent bias in order to apply proper compensation.

Most dedicated software packages such as Summitversion 4.0 (Dako Cytomation), Flowmax V 2.2 (Partec),and WinList V 5.0 (Verity Software House Inc.) functionwith manually determined values of the intensity dependentbias. In contrast, the semiautomatic determination of thecompensation value is used as a feature in the Winlist,Summit, and FloJo (V 7.5) software packages. All of thesemethods essentially work with an initial estimate of theintensity dependant bias and require operator evaluation andvalidation through visual inspection of the compensationresults. In most cases this process results in an iterativemanual refinement of the initial estimate of the intensitydependant bias and is very clearly operator dependent.

In this paper we propose a fully automated compensationalgorithm we have called Data-Driven Compensation orDDC. With this method we aim to exclude operator-associated subjectivity in defining the compensation value.To achieve this, we select for a subset of counts with thecommon characteristic of value “zero” for their primaryfluorescence. As defined above, the background fluorescenceis composed out of three factors only: autofluorescence,optical or electronic noise, and cross-over from a secondfluorochrome. Autofluorescence and noise are independentof the signal of a second fluorochrome. The cross-overcontribution however increases the intensity of the observedfluorescence proportionally to the intensity of the second flu-orochrome. This difference in contribution between “signal-independent” and “signal-dependent” elements provides fora good tool to measure the amount of cross-over. If cross-over signaling would not exist, all counts with zero primaryfluorescence would effectively be displayed on a line parallelto the abscissa or ordinate in a dot plot. Therefore, the slopeof the total fluorescence in the selected counts with zeroprimary fluorescence can serve this purpose. The resultingselected subset has a reduced variance of FITC intensity whencompared to that of all of the counts acquired as illustratedin Figures 3(a) and 3(b).


In the following section we will describe formal approachof compensation, using the DDC concept, and explain theautomatic determination of the intensity dependent bias.

2.6. Formalization of Compensation. In a 2-color flow cytom-etry experiment with single cross-over, we define a detectorDA, sensitive to a range of wavelengths of a specific fluo-rochrome A, and a detector DB, sensitive for fluorochrome B.Due to the spread of wavelengths emitted by fluorochrome B,there is cross-over (or spillover) of value SBA of fluorochromeB into the detector of fluorochrome A. The goal of compen-sation is to correct for this cross-over. The equations for thesignals picked up by the two detectors are generally expressedas [1, 12]

DA = A + SBAB, (1a)

DB = B + SABA. (1b)

These equations can be rewritten to compute the actual (orcompensated) fluorochrome value for A:

A = DA − SBADB

1− SBASAB, (2a)

B = DB − SABDA

1− SBASAB. (2b)

Since we have defined SAB = 0, there is no cross-over from Ainto DB. Therefore these two equations can be rewritten as

A = DA − SBADB, (3a)

B = DB. (3b)

2.7. DDC. In essence the DDC algorithm automaticallyselects counts with zero primary fluorescence content fromthe acquired flow cytometry data. Below we describe theautomatic selection of the zero fluorescence counts and thecalculation of the cross-over values from these counts.

As described, an NC and a TEST sample, with N =100.000 counts each, were acquired in every SLN experiment.As shown in Figure 1, each acquisition can be representedby a matrix of 2 merged vectors, DA and DB of length N.The common counts (CCs) are defined as the matchingrows (vectors of length 2) of the matrix of the NC sampleand of the TEST sample. As shown, the common countsare those counts for which the total fluorescence of bothfluorochromes A and B is identical in the NC and the TESTmatrices.

In the files every count consists of a total fluorescencesignal to which different components contribute. In a similarway the total number of counts is made up of differentclasses of counts. Three types can be identified in the NCfile: (1) negative counts with zero primary fluorescence, (2)positive counts with primary fluorescence signal generatedby nonspecific binding of nonrelevant mouse Ig (stainingbackground), and (3) counts that solely result from noiseand other flow cytometer imperfections. In a typical exper-iment less than 5% of type 2 counts are expected from

the immunostaining in the NC. In a well-calibrated andmaintained flow cytometer, the number of type 3 counts willbe less than 0.1%. In summary, the counts of the NC sampleconsist of about 95% of the type (1) counts.

The counts collected from a TEST sample consist of thesame three types as those described for the NC sample, sup-plemented with counts that contain sufficient fluorescenceintensity to be defined as “positive.” The common counts ofthe NC and TEST matrices will not include these “positive”counts, as they appear exclusively in the TEST sample files.In the common counts, any positive counts therefore mustbe of type (2). The expected amount of type (2) countsmaximize about 5% of the total counts. In conclusion,the majority of the common counts contain values of zeroprimary fluorescence for both the NC and TEST files.

Having identified the common counts with zero primaryfluorescence, we can now proceed to calculate the cross-overvalues. In the case of single cross-over from B in DA, onlyan NC with a nonrelevant Ig coupled to fluorochrome A isneeded. Each count in the CC consists then of two values: (1)an intensity value for A (DA) which holds the values for zeroprimary fluorescence (D0

A) and (2) an intensity value for B(DB). The cross-over value SBA can then be calculated fromthe CC with the rewritten (3a):

A = D0A − SBADB = 0 =⇒ SBA = D0

A

DB. (4)

These equations show that the cross-over value SBA can becalculated from the CC. For the experiments completed inthis work only (4) was used. Based on the selection of thedyes, we know that only cross-over from fluorochrome A(PI) into DB can be shown but no spillover of fluorochromeB (FITC) into DA is present. Under these conditions, dataanalysis can be limited to the NC using a nonrelevant, FITC-labeled antibody. As such the CC matrix will consist ofcounts with only zero primary fluorescence for DA (FITCdetector). For two-color experiments with double cross-over,the formula to calculate the cross-over values (SBA and SAB)can be found in Appendix A.

2.8. Correctness of Compensation. Even though we were ableto present a proper path to define compensation, no objectivemeasure exists to quantify and validate the correctness ofcompensation. Visual inspection is subjective as it dependssolely on operator experience while the RIDB value isalso visually estimated from the compensated dot plots.Herzenberg et al. [4] proposed displaying the data on alogarithmic scale [13] and compared the centre positionof the stained population with the centre position of theunstained cell population (background). Expected positionsof the centres of the unstained (sub)populations in a corre-lated fluorescence plot can be described along the respectiveaxes. These positions might be indicative for over- or under-compensation. However, a positive TEST (sub)populationwill always have a centre “above” the unstained (background)population along the same intensity axis, regardless of aproper compensation setting.


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Figure 1: Identification of the common counts as basis for the calculation of the cross-over value. The matrices for the NC (a) and TEST(b) result from an experiment with 4 counts (N) and a single cross-over from fluorochrome B in detector DA. The matching rows of theNC and TEST matrices (grey) are defined as the matrix of the Common Counts (c). The rows in the Common Counts define counts withzero primary fluorescence for fluorochrome A (D0

A). The cross-over value from fluorochrome B in DA can be calculated directly from thecommon counts. In the case as shown, 40/800 = 0.05 and 20/400 = 0.05.

3. Results

To test the DDC algorithm we conducted three experiments.In the first experiment we compared the compensationvalues obtained with DDC to those of manual compensation.All manual compensations were performed individually inthe Summit software. We consider the performance of theDDC algorithm comparable with manual compensationwhen the two sets of compensation values agree. In thesecond experiment the results of the SLN analysis are calcu-lated. These results are expressed as the percentage of positivecounts in the TEST sample. The outcome is comparedbetween the DDC and Summit paths. For these first twoexperiments a new MATLAB implementation was writtenfor the reanalysis of the cases in the DDC dataset, whichused the function FCA readfcs [14]. The only differencebetween the automated Matlab implementation and themanual analysis in Summit software is the compensationalgorithm. The Matlab implementation of DDC includes the“Trust Region” algorithm [15–17]. This algorithm calculatesthe optimal fit of the compensation trace line through theCC. Alternatively, the manually determined compensationtrace line, using the Summit software, is based on a visuallydetermined optimal fit through all available counts. Aftercompensation is completed, a doublet discrimination step isapplied. This doublet discrimination will not influence thefirst experiment, although it slightly affects the percentagepositive counts in the second experiment.

The third experiment is performed to express thecorrectness of compensation. We herewith propose a newoption, building on earlier work. Two methods have beensuggested to achieve proper compensation. The first methoduses a single stained control (SSC) for each fluorochromein the panel [1, 3, 4, 12, 18]. The second method uses anisotype control only [2]. In our 2-color experiments we haveonly a cross-over from PI in the FITC channel. This setupcompares more with the second method (isotype control—implemented as NC) than with the first (SSC method—sample containing only PI). As described above, within theNC, we expect less than 5% positive FITC counts in thissample (background signal), the observed slope (or trendline) therefore of the CC from a NC and SSC shouldbe approximately the same as the slope (or trend line)observed of the CC from a NC and TEST. When the two

slopes agree, the calculated compensation using the DDCprocedure leads to a correct compensation value. Since wedo not routinely apply an SSC for the sentinel test in ourlaboratory, we acquired an additional 45 cases with an extranSSC (containing only PI) for the purpose of this thirdexperiment.

3.1. Comparative Evaluation of the Compensation Values.To test the capability of the DDC algorithm to correctlycalculate the compensation values, we compared thesecalculated values against the manually determined values.After linear transformation of the Summit compensationvalues SSUMMIT into appropriately rescaled values SSUMMIT∗

(see Appendix B), the linear relation between the pairedcompensation values (Summit and DDC) is defined by theregression line

SSUMMIT∗ = 0.90, SDDC + 0.0049 (5)

as illustrated in Figure 2. This figure shows the rescaled man-ually determined compensation values SSUMMIT∗ (on theordinate) against the compensation values (SDDC) generatedby DDC (on the abscissa). The dots indicate the pairedcompensation values, expressed as the percentage cross-overfor each case in the dataset. The combination of the highcorrelation (R-square = 0.90) with the limited scatter aroundthe regression line (Root Mean Squared Error = 0.0034)indicates that the DDC method generates compensationvalues that are very comparable with those determinedmanually. As indicated by the regression slope of 0.90, theDDC-generated compensation values are slightly higher thanthe values generated by the Summit software. The horizontalclustering of the “Summit value” dots in the graph reflectsthe need of an operator to resort to rounded compensationvalues upon manual interaction.

A total of five cases (out of 152) fall outside the95% confidence interval. Two of these five cases are veryclose together under the lowest prediction bound, andtheir mutual characteristic is high background signal ofthe NC sample. This high nonspecific binding in theseNC samples leads to an increase of CC values. Since thisnonspecific reactivity induces a shift towards higher FITCintensities, fitting the compensation trace line leads to ahigher compensation value, and thus to overcompensation.


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Figure 2: Results of a regression analysis of the manually deter-mined compensation values using Summit V4.0 (S-SUMMIT,ordinate) and the automatic compensation values calculated usingthe DDC algorithm (S-DDC, abscissa), for the negative controlsamples. All compensation values are calculated on 100.000 cellularevents. A regression line (black solid line) is fitted through allthe admissible data points. The dashed lines represent the 95%prediction bounds of the fit.

The other three cases (above the highest prediction bound)were reanalyzed by the two operators. They both turned outto be manually overcompensated in the Summit procedure.

3.2. Comparative Evaluation of the TEST Results. The objec-tive of the SLN procedure is to determine the percentagepositive counts in a TEST sample compared to its NC. There-fore a second regression analysis was performed to comparethe percentage positive counts found with the originalSLN Summit procedure (pos Summit) versus the procedurewith incorporation of the DDC algorithm (pos DDC). Theregression line is defined by

pos Summit = 0.90∗ pos DDC + 0.042. (6)

Also in this set, a good match between the paired resultswas found. The high correlation value (R-square = 0.98)and the limited scatter around the regression line (RootMean Squared Error = 0.084) indicate that the results of theanalysis with using the automated DDC method are verycomparable with the results from the manual compensationmethod. Only six cases out of the 152 fall outside the 95%confidence interval. Reanalysis of these six cases by the twooperators revealed four cases for which lower Summit-basedcompensation values were used for the NC as compared tothe TEST. Over-compensation of the TEST data resulted ina lower percentage of positive counts. This compensation

error is a common artifact and well documented in theliterature [1, 5]. The remaining two cases were correctlycompensated by the DDC algorithm as re-analysis with theSummit software revealed that both cases were indeed under-compensated through visual inspection. It appeared thatwith applying just 0.1% additional compensation decreasedthe height of the threshold in the NC sample. This operationresulted in an increase in the percentage of the positivecounts in the TEST sample, minimizing the differencesbetween the Summit and the DDC algorithm outcomes.

3.3. The Correctness of Compensation. Even though com-pensation values might agree between the two differentmethods applied, it doesnot automatically imply that thesecompensation values are correct. As mentioned before weacquired an additional 45 cases, stained according the SSCconcept. The compensation values found with using the CCof the SSC and the NC (set 1) can thus be compared with theones obtained using the CC of the NC and TEST (set 2).

The 2 sets of compensation values show no Gaussiandistribution and are highly correlated (R-square = 0.9651,RMSE = 1.5× 10−3). The spread between the maximum andminimum compensation values in both sets is comparable,4.3% in the first set and 4.2% in the second set. Thereis no statistical evidence for different compensation valuesin the two sets, based on 45 cases. However, all the com-pensation values, except one, in the first set were lowerthan their matching compensation values in the second set.This difference is also reflected in the mean compensationvalues, which are 4.9% for the first set and 4.7% for thesecond set. Despite the statistical insignificant compensationvalues between the two sets, the visual effect of applyingtwo different compensation values to the same sample isevident.

The different compensation values within one sampleare illustrated in Figures 3(a) and 3(b) by the two whitecompensation trace lines. These two illustrations show theuncompensated dot plots of an isotype NC (upper left graph)and TEST (upper right graph) of one of the additional 45cases. Each graph plots all counts (grey dots) representedby their FITC value (ordinate) as a function of the PI value(abscissa). The common counts are represented by the blackdots. The compensation trace line is defined as the best fittingline through the CCs. The dotted compensation trace line isthe result of fitting a line through the CC of the NC and SSC(the SSC is not visualized). The full compensation trace lineis fitted through the CC of the NC and the TEST values. Thevisual effect of applying two different compensation values tothe test sample from Figure 3(b), is illustrated in Figures 3(c)and 3(d). In Figure 3(c) the compensation result of the TESTis illustrated, after applying the dotted compensation traceline. Figure 3(d) illustrates the compensated events afterapplying the straight compensation trace line. The medianvalues of the 2C–10C peaks are illustrated with an “X.”The main visual difference between Figures 3(c) and 3(d)is the distribution of the median values. These medians aredistributed along the full compensation trace line.


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Test compensated with DDC

(d)

Figure 3: (a) shows events of a negative control (NC). (b) shows the events of the matching TEST. Both graphs are uncompensated 2-colorplots, from sentinel lymph node (SLN) tissue. (c) shows the TEST after compensation, using a trace line fitted through the common countsof the NC and SSC (dashed line). (d) shows the TEST values, after compensation with a compensation trace fitted through the CC of theNC and the TEST (the full line). Each dot plot consists of 100.000 counts. The grey dots represent the individual counts in each dot plot.The black dots represent the common counts. The median values of each of the 5 distinct clusters (ploidy level 2C, 4C, 6C, 8C, and 10C)are marked with an “X.” For optimal visual representation, the pairs of compensation trace lines are white in the upper graphs and blackin the lower graphs. Note that the 2 different compensation trace lines seem to be parallel in (a) and (b), which is an optic illusion becausethe ordinate is logarithmic. In the linear domain these 2 compensation trace lines diverge. The dot plots represent logical (T = 10000,W = 0.5, M = 4.5) [13], FITC fluorescence (ordinate) versus linear PI fluorescence (abscissa). The negative control was incubated with anegative mouse Ig and labeled with FITC, and the test case was incubated with a monoclonal cytokeratin antibody (clone MNF116). In allcases the DNA content was labeled with PI. There was only cross-over from PI in the FITC detector, which can be seen in the slope of thedotted compensation trace lines, and no cross-over from FITC in the PI detector, because no slope, in vertical direction, can be seen in theFITC positive counts in the 2C, 4C, 6C, 8C, and 10C clusters in (b). Ideally, the CC would form a straight line, slightly deformed by thelogarithmic scaling of the ordinate. In practice the ideal line is scattered due to the influence of auto fluorescence, photon count statisticsand noise. Additional peaks of positive counts are visible in the 2C, 4C, 6C, 8C, and 10C clusters in the TEST, which are not included in theCC.


4. Discussion

We have evaluated an automated data-driven approachto fluorescence compensation in a two-color setting. Allother compensation methods used thus far involve operatorinteraction and limit a fully automated data analysis. In orderto provide confirmation and validation for the proposedmethodology, we have used two methods that are commonlyused in flow cytometry laboratories as reference, the Summitand the Winlist software. We have compared the outcomeof the proposed DDC method against the outcome of thesereference methods. The results show that (1) two colorflow cytometry compensation and analysis of sentinel lymphnodes in Summit and DDC lead to comparable results,despite that Summit uses different compensation valuesthan DDC does, (2) the effects of different approaches tocalculate compensation values based on the CC can bevisualized within one sample, (3) DDC is a data-drivenmethod that combines the information of a NC or SSCwith a TEST to calculate sample-specific trace lines, whichenables the possibility to automatically analyze large datasetsof individual cases batchwise. This is where DDC improvescurrent compensation methods.

According to the Summit reference guide, the Summitsoftware uses a variant of our formulas (1a) and (1b) for thecalculation of the compensation values [19]. That variant isstated as

DA = A + SBABtrue, (7a)

DB = B + SABAtrue. (7b)

In these modified formulas (7a) and (7b) there is a differencebetween the acquired values for A and B and the unknowntrue values Atrue and Btrue. The equations proposed heremake use of the unknown values “Atrue” and “Btrue.” In thework presented here, we have selected the dye combinationsuch that the initial assumption could be stated as SAB = 0.From this limitation it follows that DB = B = Btrue as can beseen from Figure 3(b). Under this specific condition, (7a) canbe rewritten to confirm (3a). Therefore, the compensationmathematics in the Summit software should behave exactlylike the equations used by DDC. However, our resultsclearly show that the same compensation value applied to(3a) or to the Summit equation (7a) always resulted indifferent distributions of compensated counts. This can beobserved as a visual difference in the RIDB. This differencein distribution is not explained by the information obtainedfrom the Summit reference guide [19].

To better understand the different distributions in thecompensated dot plots, we have recompensated 10 data filesusing the Winlist software and have compared these resultswith data obtained using Summit. The Winlist option waschosen as a valuable alternative, as it is an independent,commercially available and commonly used software. Thecompensation algorithm in Winlist is based also, as we havedone in the DDC approach, on (1a) and (1b) [20]. In orderto allow a correlation between the sets of compensationvalues obtained using the Summit and the Winlist software,a rescaling of the Summit compensation units was required

to units that are used by Winlist. Appendix B contains thedetails of this conversion, including the regression analysis.This rescaling of the Summit compensation values by anindependent compensation software enabled us to perform avalidated comparison with the DDC method using identicalcompensation units. The observed correlation between therespective compensation values provides clear evidence thatthe DDC method can replace manual compensation.

The DDC method as proposed in this work makes itpossible to objectively compare the effect on fluorescencecompensation results when using different approaches.

In the experiments performed in our laboratory, bothFITC and PI are used for simultaneous staining. The com-pensation performed requires an estimate of the cross-overof signal from the PI dye into the FITC detector (FL1).This cross-over effect and its estimate were also discussed inearlier work [2]. In this work we therefore used a NC andTEST sample setup for the direct comparison between valuesobtained through the conventional analysis and through theautomated calculation via the DDC algorithm.

One alternative path in the literature claims that thepercentage cross-over can only be estimated with using anSSC [1, 4, 5]. Incorporation of an SSC, only containingPI, into the DDC algorithm approach was made to alsocomply with this alternative path. The results as shown inSection 3.3 indicate that using the SSC setup, with DDC,leads to slightly lower compensation values than usingthe NC setup. This difference in outcome between bothapproaches is illustrated in Figures 3(c) and 3(d). Thesetwo dot plots illustrate the difference in appearance of thecompensated counts. The increasing median values alongthe trace line, marked with an “X,” in Figure 3(c) maysuggest under-compensation. However, our results indicatethat the RIDB shift between the two compensated plotsis caused by the included FITC component in the isotypeNC. This FITC component elevates all the counts in theisotype NC, compared to the SSC. This elevation causesthe increased compensation value. Therefore on strictlytheoretical grounds applying DDC to an isotype NC andTEST leads to overcompensation. However, in this specificsituation this will result in a more horizontal distributionof the median values. This horizontal distribution of themedian values makes application of a horizontal thresholdmore suitable for discrimination between FITC positive andnegative counts.

Although we found a better distribution of median valuesafter overcompensation, in a specific two color setting, thisdoes not imply that overcompensation always yields betterresults. When compensated values of one fluorochromeinfluence the compensated values of other fluorochromes,overcompensation is not recommended. On the other handwhen the fluorochromes FITC, PI, and APC are combined,there is only cross-over from PI in FITC and from PI inAPC. In this specific setting the compensated FITC and APCvalues do not influence each other, therefore both can beautomatically compensated with DDC, based on two pairsof isotype controls and their TEST.

Batchwise compensation with currently available soft-ware is only possible with stable compensation values, which


(a) (b) (c)

——

——

8008500

2042

850023 704

250800401 8500

421001

31

250800723401

42 (D0A)

250 (D0B)

DA DB DA DB DA DB

Negative control TEST Common counts

Figure 4: Illustration of the identification of the common counts and the calculation of the cross-over value. Each 2-color experimentconsists of 2 acquisitions; a negative control (NC) and a TEST. Matrices are shown for the NC (a) and TEST (b) based on an experimentwith a total of 4 counts. Cross-over exists from fluorochrome B into detector DA and from fluorochrome A into detector DB . The matchingrows of the NC and TEST matrices (grey) are defined as the matrix of the Common Counts (c). The CCs matrix contains counts withzero primary fluorescence for fluorochromes A (D0

A) and B (D0B). Separation is required into counts with zero primary fluorescence for

fluorochrome A and counts with zero primary fluorescence for B. Cross-over values can be calculated directly from the common count. Inthis example, SBA = 42/800 = 0.05 and SAB = 250/8500 = 0.03.

can be monitored by daily calibration and performancetracking. However, PI binds noncovalently to DNA andtherefore the intensity of the PI signal is dependant on thecell concentration. Given the same amount of PI, single-cellsuspensions with high cell concentrations result in lower PIintensities per cell. The result is a shift of the acquired FL3-ahistogram to the left, as compared to samples that containlower cell concentrations. DNA acquisitions are thereforestandardized by adapting the voltage of the PMT of the firstacquisition in each tumour sample, until the median valueof the first peak falls in channel 200 of a 1024-resolution,linear acquired, DNA histogram [21]. Variable PMT settingsbetween cases lead to case-specific compensation values.The work presented here takes the element of case-specificcompensation values into account. The observed correlationof the compensation values between the manual analysis inSummit and the automated DDC analysis clearly shows thatthe proposed DDC approach can even calculate differentcompensation values batchwise. This opens the path tocomplete automated data analysis for DNA phenotype acqui-sitions.

The evolution from limited multiparameter to full poly-chromatic flow cytometry comes with increasing flow cytom-etry colors and parameters [22]. This leads to increaseddata output in more dimensions than the human brain cancomprehend, and we will therefore have to rely on computersfor help with complex matters including compensation. Theproblem of current compensation algorithms is that they aresolely based on mathematics [1]. Alternatively classificationalgorithms like artificial neural networks (ANNs) supportvector machines (SVMs) or k-means clustering have thepotential to analyze high-dimensional data sets. Howeverthey lead to black-box analysis. It is only recently that classi-fication algorithms have been used with integrated operatorexperience in flow cytometry, either for the selection ofa training set supporting ANN-based gating [23] or as aparadigm for automated density based merging of dataclusters [24].

The DDC approach presented here also integrates oper-ator experience to appropriately deal with sample-specificvariables. The set of CC represents the specific area in the

traditional approach to set a compensation trace line [2, 10,25] and can easily be visualized in a dot plot. Visualizationof data analysis is of psychological importance to opera-tors and scientists, giving them the possibility to interact,when specific or unexpected distributions appear upon dataacquisition. All current methods however require operatorintervention, sometimes iterative. This is time consuming,depends on operator experience, and can lead to error, evenwhen expertise is available. Objectivity and quantificationare essential parameters in the onset to automation of theprocess. Based on the work presented, we conclude that DDCimproves operator-associated objectivity in fluorescencecompensation and facilitates visual representation of datasubsets (CC).

We expect that the implementation of DDC will improvethe use of classification algorithms by generating training setswith data that have been corrected for case specific variability.

Appendices

A. Formalization of Compensation for 2-ColorFlow Cytometry with Double Cross-Over

In the case of 2-color experiments with double cross-over,a NC uses two non relevant antibodies for backgroundstaining, one coupled to fluorochrome A and one coupledto fluorochrome B. In this experiment the CC will containa combination of counts with zero primary fluorescence forfluorochromes A (D0

A) and B (D0B) (see Figure 4).

In a dot plot of DA against DB, the CC will form twopopulations with two different slopes SBA and SAB. Withthese two populations separated, SBA can be calculated withthe help of (A.1a). Similarly, SAB can be calculated using therewritten equation (A.1b):

A = D0A − SBADB

1− SBASAB= 0 =⇒ D0

A − SBADB = 0 =⇒ SBA = D0A

DB,

(A.1a)

B = D0B − SABDA

1− SBASAB= 0 =⇒ D0

B − SABDA = 0 =⇒ SAB = D0B

DA.

(A.1b)


Table 1: The compensation values obtained on 10 data files usingSummit and Winlist software. The compensation value correctsfor spillover of the PI dye (detected in FL3) into the FL1 detector(FITC).

Compensation valueSummit

Compensation valueWinlist

1.0 0.05

0.9 0.04

1.35 0.07

1.45 0.08

1.65 0.09

1.50 0.08

1.20 0.07

0.80 0.04

0.80 0.04

1.1 0.05

B. Rescaling of the Compensation ValuesFound in Summit

To compare the manual compensation values generated inthe Summit software with those obtained with the DDCalgorithm, the compensation units need to have a quantifi-able relationship. Unfortunately, the unit of compensationin the Summit software is not documented. To properlydefine this unit, we have compared the “Summit” units tothose units as defined in the Winlist software. This softwareuses compensation algorithms described by Bagwell. Thesealgorithms have been extensively documented [1–3, 5, 10,25].

We used 10 of the acquired data files and reanalyzed theseusing the Winlist software. Table 1 lists the compensationvalues obtained with the two software models. The regressionanalysis of the manual compensation values obtained usingthe Summit software and the compensation values obtainedusing Winlist revealed the following linear relation:

SSUMMIT∗ = 0.062∗ SSUMMIT − 0.011, (B.1)

where R-square = 0.96, RMSE = 0.0040, with SSUMMIT

being the compensation value as obtained by Summit andSSUMMIT∗ the rescaled compensation value.

Acknowledgments

The authors acknowledge E. O. Postma, R. Langelaar, and F.Nauwelaers for their critical comments on this paper.

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